Name: ____________________________________
Mock Final 1 NON -Calculator Questions
Mock Final #1
NON
CALCULATOR
The following practice exam is intended to prepare you for the Final exam during
May 23rd and May 24th
The level of difficulty is intended to model the final exam for this course.
For all questions in this booklet you will NOT be able to use your calculator.
This will be completed in class and checked for homework
1. Two ordinary, 6-sided dice are rolled at a time, and the roll outcomes are noted each time.
(a)
Complete the tree diagram by entering probabilities and listing outcomes.
6
Outcomes
...............
.......
6
.......
.......
not 6 ...............
6
.......
...............
.......
not 6
.......
(b)
Find the probability of getting one or more sixes.
not 6 ...............
[4]
Working
2. Let 𝑓(𝑥) = (𝑥 − 5)3
a. Find 𝑓 −1 (𝑥)
[3]
b. Hence find (𝑓 ∘ 𝑓
−1
)(8)
[3]
Working
3. If A is an obtuse angle in a triangle and sin A = 5 , calculate the exact value of sin 2A.
13
[4]
Working
4. The following box-and whisker plot represents the examinations cores of a group of students.
a. Write down the median score.
[1]
The range of the scores is 47 marks, and the interquartile range is 22 marks.
b. Find the value of
i. c;
ii. d.
Working
[4]
5. An arithmetic sequence has the first term lna and a common difference ln3.
The 13th term in the sequence is 8 ln 9. Find the value of a.
[6]
Working
6. Let 𝑓 ′ (𝑥) = 6𝑥 2 − 5. Given that f(2) = -3, find f(x).
Working
[6]
𝑥
7. The following diagram shows the graph of 𝑓(𝑥) = 𝑥 2 +1 for 0 ≤ 𝑥 ≤ 4, and the line x = 4.
Let R be the region enclosed by the graph of f, the x-axis and the line x = 4.
Find the area of R.
Working
8. The following diagram shows triangle ABC.
⃗⃗⃗⃗⃗ ||𝐴𝐶
⃗⃗⃗⃗⃗ | = 10. Find the area of triangle ABC.
Let ⃗⃗⃗⃗⃗
𝐴𝐵 ∙ ⃗⃗⃗⃗⃗
𝐴𝐶 = −5√3 and |𝐴𝐵
Working
9. The following diagram shows part of the graph of a quadratic function f.
The vertex is at (1,-9) and the graph crosses the y-axis at the point (0,c). The function can be written in the
form f(x) = (𝑥 − ℎ)2 + 𝑘.
a) Write down the value of h and of k.
[2]
b) Find the value of c
[2]
Let g(x) =−(𝑥 − 3)2 + 1. The graph of g is obtained by a reflection of the graph of f in the axis followed by a
translation of (𝑝𝑞).
c) Find the value of p and of q
[5]
d) Find the x-coordinates of the points of intersection of the graphs of f and g.
[7]
10. Fred makes an open metal container in the shape of a cuboid, as shown in the following diagram.
Working